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## [Axiom-math] Re: [Axiom-developer] Summing over a list

 From: Martin Rubey Subject: [Axiom-math] Re: [Axiom-developer] Summing over a list Date: 23 May 2007 15:50:39 +0200 User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

```Dear Alasdair,

(redirecting to axiom-math, where usage questions belong)

> Given two lists,for example:
>
> z:=[1,2,3,4,5,6]
> w:=[1,0,0,1,1,1]
>
> it seems that the sum of the pairwise product is obtained by
>
> reduce(+,[z.i*w.i for i in 1..6])3B

yes. Or, if you prefer

reduce(+, [ez*ew for ez in z for ew in w])

or, if you are really thinking of the standard inner product

dot(z, w)

> which is all very well.  But why doesn't
>
> sum(z.i*w.i,i=1..6)
>
> work?  I mean, sum(i^2,i=1..6) is fine.

For a (very long) explanation see

http://wiki.axiom-developer.org/IndexedVariables

Short explanation: unlike Mma or Maple, in axiom evaluation is extremely
simple: first the arguments are evaluated, then the function.  So, in your
case, first axiom tries to evaluate

z.i*w.i

and

i=1..6

but there is no operation elt (which the dot is syntactig sugar for) that takes
a list and a symbol -- try to type z.i into the interpreter!  To make things
clearer, note that there *is* an operation "=" that takes a symbol and a
segment.

Hope that helps,

Martin

```